PhD Chapter 1

Campaign 2017 - Analyses and regressions

This series of files compile analyses done for the specific analysis of Chapter 1, for the regional campaign of 2017.

All analyses have been done with PRIMER-e 6 and R 4.0.4.

Click on the table of contents in the left margin to assess a specific analysis.
Click on a figure to zoom it

We used data from subtidal ecosystems (see metadata files for more information). Only stations that have been sampled both for abiotic parameters and benthic species were included.

Selected variables for the analyses:

Depth of the station: depth (only for ANCOVAs)
Percentage of organic matter: om
Percentage of gravel: gravel
Percentage of sand: sand
Percentage of silt: silt
Percentage of clay: clay
Concentration of arsenic: arsenic
Concentration of cadmium: cadmium
Concentration of chromium: chromium
Concentration of copper: copper
Concentration of iron: iron
Concentration of manganese: manganese
Concentration of mercury: mercury
Concentration of lead: lead
Concentration of zinc: zinc
Specific richness: S(only for 500 µm communities)
Total density of individuals: N (only for 500 µm communities)
Shannon’s diversity: H (only for 500 µm communities)
Piélou’s evenness: J (only for 500 µm communities)

We only considered 500 µm communities for these analyses. Abundances of Bipalponephtys neotena (Bneo) and Nematoda (Nema) were also considered (see IndVal and SIMPER results).

Heavy metal concentrations for campaign 2017 have been kriged from the values collected at campaigns 2014 and 2016. As data is missing for metal concentrations outside BSI, two Designs have been used:

Design 1: stations at BSI, MR with habitat parameters
Design 2: stations at BSI with heavy metal concentrations.

1. Permutational Analyses of Covariance

Results of univariate PermANCOVAs on parameters and multivariate PermANCOVA on the whole benthic community with depth as covariate are presented in the table below. Variables have been standardized by mean and standard-deviation, and taxon densities were (log+1) transformed.

Variable	Condition	Depth
om	S
gravel
sand
silt	S
clay
S (500 µm)		S
N (500 µm)
H (500 µm)		S
J (500 µm)		S
ALL SPECIES (500 µm)	S	S

2. Similarity and characteristic species

Let’s have a look at the $\beta$ diversity within our conditions and sites.

Results of the PERMDISP routine are shown below (mean and SE of the deviation from centroid for each group, i.e. multivariate dispersion), along with the mean Bray-Curtis dissimilarity for each group. Taxon densities were (log+1) transformed and PRIMER was used to do the PERMDISP.

Mean within-group Bray-Curtis dissimilarity for each condition or site
	Mean deviation	SE of deviation	Mean BC dissimilarity
HI	57.5	1.64	0.829
R	48.8	2.43	0.71

Significative differences in dispersion have been detected between HI and R (p = 0.0053).

The following analyses allowed to detect species as characteristic of each condition. We used results from PRIMER to justify further their choice.

##                        cluster indicator_value probability
## bipalponephtys_neotena       1          0.6390       0.001
## macoma_calcarea              1          0.5583       0.004
## goniada_maculata             1          0.2917       0.028
## nematoda                     2          0.6565       0.005
## echinarachnius_parma         2          0.6524       0.001
## crenella_decussata           2          0.5836       0.001
## ecrobia_truncata             2          0.3333       0.005
## mesodesma_arctatum           2          0.2667       0.016
## solariella_sp                2          0.2000       0.039
## 
## Sum of probabilities                 =  55.401 
## 
## Sum of Indicator Values              =  13.26 
## 
## Sum of Significant Indicator Values  =  4.18 
## 
## Number of Significant Indicators     =  9 
## 
## Significant Indicator Distribution
## 
## 1 2 
## 3 6

SIMPER results (mean Bray-Curtis between-group dissimilarity: 0.872)
	average	sd	ratio	ava	avb	cumsum
nematoda	0.0743	0.0621	1.2	0.879	2.08	0.0852
echinarachnius_parma	0.0618	0.0632	0.977	0.361	1.59	0.156
bipalponephtys_neotena	0.0556	0.0485	1.15	1.78	0.193	0.22
eudorellopsis_integra	0.0358	0.0494	0.724	1.08	0.119	0.261
crenella_decussata	0.0346	0.0352	0.983	0.0289	1.03	0.3
mesodesma_arctatum	0.0338	0.064	0.528	0	0.751	0.339
macoma_calcarea	0.0316	0.0323	0.977	1.03	0.0462	0.375
harpacticoida	0.0283	0.0325	0.872	0.801	0.258	0.408
phoxocephalus_holbolli	0.0282	0.0329	0.857	0.411	0.658	0.44
amphipoda	0.0234	0.0274	0.852	0.483	0.346	0.467
pholoe_sp	0.0215	0.0249	0.866	0.413	0.434	0.492
ameritella_agilis	0.018	0.0252	0.715	0.132	0.451	0.512
ecrobia_truncata	0.0168	0.0321	0.525	0	0.575	0.532
ennucula_tenuis	0.0164	0.022	0.742	0.401	0.212	0.55
ischyrocerus_anguipes	0.0155	0.0327	0.475	0.406	0.13	0.568
akanthophoreus_gracilis	0.0154	0.0263	0.584	0.389	0.193	0.586
hiatella_arctica	0.015	0.0309	0.483	0.0747	0.368	0.603
ostracoda	0.013	0.0195	0.664	0.207	0.258	0.618
cistenides_granulata	0.0129	0.0202	0.641	0.233	0.212	0.633
axinopsida_orbiculata	0.0117	0.025	0.47	0.361	0	0.646
thracia_septentrionalis	0.0117	0.0185	0.633	0.183	0.266	0.66
mysella_planulata	0.0117	0.0263	0.445	0	0.333	0.673
sabellidae_spp	0.0112	0.0323	0.348	0.361	0.0462	0.686
leucon_leucon_nasicoides	0.0107	0.0237	0.454	0.294	0	0.698
nephtyidae_spp	0.0107	0.0176	0.608	0.274	0.0462	0.71
orchomenella_minuta	0.0102	0.019	0.539	0.0578	0.212	0.722
nephtys_caeca	0.00966	0.0194	0.497	0.116	0.119	0.733
goniada_maculata	0.00965	0.0165	0.585	0.286	0	0.744
mytilus_sp	0.0092	0.0268	0.342	0.287	0	0.755
solariella_sp	0.0089	0.0205	0.435	0	0.29	0.765
pontoporeia_femorata	0.00864	0.0245	0.352	0.225	0	0.775
parvicardium_pinnulatum	0.00863	0.0164	0.527	0.0578	0.227	0.785
caprella_septentrionalis	0.00844	0.029	0.291	0.34	0	0.795
protomedeia_fasciata	0.00786	0.0165	0.478	0.241	0	0.804
lamprops_fuscatus	0.00694	0.0128	0.543	0.207	0.0462	0.811
pholoe_longa	0.00605	0.0189	0.319	0.11	0.0732	0.818
protomedeia_grandimana	0.00592	0.0173	0.342	0.213	0	0.825
astarte_sp	0.00588	0.013	0.454	0.0747	0.119	0.832
chone_sp	0.00567	0.0282	0.201	0.107	0	0.838
monoculopsis_longicornis	0.00559	0.0144	0.388	0.125	0.0924	0.845
ophelia_limacina	0.00551	0.0112	0.494	0.0289	0.166	0.851
glycera_sp	0.00542	0.0171	0.317	0.116	0	0.857
chaetodermatida	0.00541	0.0117	0.462	0.144	0.0462	0.864
nephtys_incisa	0.00535	0.0126	0.423	0.104	0.0462	0.87
maldanidae_spp	0.00472	0.0156	0.303	0.113	0.0462	0.875
aceroides_aceroides_latipes	0.00452	0.0111	0.406	0.144	0	0.88
quasimelita_formosa	0.00447	0.0122	0.366	0.125	0	0.885
sipuncula	0.00428	0.0122	0.35	0	0.0924	0.89
euchone_sp	0.00426	0.0207	0.206	0.146	0	0.895
anthozoa	0.00409	0.0111	0.369	0	0.119	0.9

3. Regressions

3.1. Data manipulation

For the following analyses, independant variables are habitat parameters and heavy metal concentrations, dependant variables are diversity indices. Variables have been standardized by mean and standard-deviation.

3.1.1. Identification of outliers

To identify stations that are not consistent with the others, we used the multivariate Cook’s Distance (CD) on the uncorrelated variables. A significative threshold of 4 times the mean of CD has been established.

Design 1

We identified stations 188, 194 and 228 as general outliers. They have been deleted for the following analyses of Design 1.

Design 2

We identified stations 132 and 154 as general outliers. They have been deleted for the following analyses of Design 2.

3.1.2. Correlations between predictors

Correlations have been calculated with Spearman’s rank coefficient.

Design 1

According to these results, the following variables are highly correlated ($|\rho|$ > 0.80) so they have been considered together in the regressions of Design 1:

sand and silt (silt deleted)

Correlation coefficients between habitat parameters (Design 1)
	om	gravel	sand	silt	clay
om	1	-0.365	-0.791	0.877	0.119
gravel	-0.365	1	0.015	-0.325	0.183
sand	-0.791	0.015	1	-0.896	-0.47
silt	0.877	-0.325	-0.896	1	0.212
clay	0.119	0.183	-0.47	0.212	1

Design 2

Many variables are highly correlated ($|\rho|$ > 0.80), but we have considered the following together in the regressions of Design 2:

chromium, iron and manganese (iron and manganese deleted)
copper, lead and zinc (copper and zinc deleted)

We decided to keep arsenic, even though it is correlated with the copper/lead/zinc group, to stay consistant with the 2014 and 2016 campaigns.

Correlation coefficients between heavy metals concentrations (Design 2)
	arsenic	cadmium	chromium	copper	iron	manganese	mercury	lead	zinc
arsenic	1	0.658	0.838	0.801	0.701	0.598	0.438	0.8	0.874
cadmium	0.658	1	0.809	0.467	0.719	0.794	0.288	0.806	0.777
chromium	0.838	0.809	1	0.811	0.871	0.84	0.406	0.889	0.945
copper	0.801	0.467	0.811	1	0.688	0.573	0.308	0.805	0.896
iron	0.701	0.719	0.871	0.688	1	0.834	0.182	0.71	0.848
manganese	0.598	0.794	0.84	0.573	0.834	1	0.208	0.679	0.77
mercury	0.438	0.288	0.406	0.308	0.182	0.208	1	0.488	0.37
lead	0.8	0.806	0.889	0.805	0.71	0.679	0.488	1	0.924
zinc	0.874	0.777	0.945	0.896	0.848	0.77	0.37	0.924	1

3.2. Univariate regressions

We used linear models for the regressions on diversity indices. Outliers and correlated variables were removed from these analyses. Variables have been standardized by mean and standard-deviation (coefficients need to be back-transformed to be used in predictive models).

3.2.1. Simple regressions

These analyses have been do to explore the relationships between variables. As it is a huge number of results to interpret, only multiple regressions will be included in the article (see below).

Depth has been shown important for several parameters in the ANCOVAs, so here are the corresponding scatterplots.

Design 1

Adjusted R-squared of simple regressions for Design 1
	om	gravel	sand	clay
S_500	-0.02767	0.01197	-0.001571	-0.02831
N_500	-0.0185	-0.02098	-0.02294	0.002618
H_500	-0.009374	-0.0139	0.02245	0.02041
J_500	0.02241	-0.02941	0.005738	0.02843

p-values of simple regressions for Design 1
	om	gravel	sand	clay
S_500	0.8117	0.241	0.3378	0.8497
N_500	0.5501	0.5997	0.6458	0.3034
H_500	0.417	0.4757	0.1882	0.1973
J_500	0.1883	0.9884	0.2806	0.1639

Design 2

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3.2.2. Multiple regressions

This section presents analyses done to determine which variables are the most important to explain the parameters.

We identified which variables were selected after an AIC procedure to predict the best the parameters. Results of the variable selection, according to AIC, are shown on the tables below:

for the model of Design 1

Variable (or combination)	S_500	N_500	H_500	J_500
om				+
gravel				+
sand/silt				+
clay				+
Adjusted $R^{2}$	0	0	0	0.06

for the model of Design 2

Variable (or combination)	S_500	N_500	H_500	J_500
arsenic	-	-	-
cadmium		+
chromium/iron/manganese	-		-	-
mercury	-	-
lead/copper/zinc	+		+	+
Adjusted $R^{2}$	0.24	0.26	0.24	0.09

Details of the regressions, with diagnostics and cross-validation, are summarized below.

Design 1

Richness

## FULL MODEL

## Adjusted R2 is: -0.06

Fitting linear model: S_500 ~ om + gravel + sand + clay
	Estimate	Std. Error	t value	Pr(>\|t\|)
(Intercept)	0.09546	0.1757	0.5434	0.5907
om	-0.2095	0.5347	-0.3918	0.6979
gravel	0.07971	0.2617	0.3046	0.7627
sand	-0.3523	0.5343	-0.6593	0.5146
clay	-0.1332	0.2967	-0.4489	0.6566

## RMSE from cross-validation: 10.96324

Variance Inflation Factors
	om	gravel	sand	clay
VIF	2.3	1.55	2.93	1.76

## REDUCED MODEL

## Adjusted R2 is: 0

Fitting linear model: S_500 ~ 1
	Estimate	Std. Error	t value	Pr(>\|t\|)
(Intercept)	0.07403	0.1675	0.4419	0.6613

## RMSE from cross-validation: 0.9974367

Quitting from lines 330-332 (C1_analyses_17B.Rmd) Error in Qr$qr[p1, p1, drop = FALSE] : indice hors limites De plus : Warning messages: 1: In CVlm(data = lm_out$model, form.lm = lm_out, m = 5, printit = F) :

As there is >1 explanatory variable, cross-validation predicted values for a fold are not a linear function of corresponding overall predicted values. Lines that are shown for the different folds are approximate

2: In CVlm(data = lm_out$model, form.lm = lm_out, m = 5, printit = F) :

Density

## FULL MODEL

## Adjusted R2 is: -0.06

Fitting linear model: N_500 ~ om + gravel + sand + clay
	Estimate	Std. Error	t value	Pr(>\|t\|)
(Intercept)	0.03898	0.1774	0.2197	0.8275
om	-0.4389	0.54	-0.8128	0.4225
gravel	-0.07614	0.2642	-0.2882	0.7751
sand	-0.3968	0.5396	-0.7354	0.4676
clay	-0.34	0.2996	-1.135	0.2652

## RMSE from cross-validation: 17.81878

Variance Inflation Factors
	om	gravel	sand	clay
VIF	2.3	1.55	2.93	1.76

## REDUCED MODEL

## Adjusted R2 is: 0

Fitting linear model: N_500 ~ 1
	Estimate	Std. Error	t value	Pr(>\|t\|)
(Intercept)	0.0233	0.1689	0.1379	0.8911

## RMSE from cross-validation: 1.082179

Quitting from lines 342-344 (C1_analyses_17B.Rmd) Error in Qr$qr[p1, p1, drop = FALSE] : indice hors limites De plus : Warning messages: 1: In CVlm(data = lm_out$model, form.lm = lm_out, m = 5, printit = F) :

2: In CVlm(data = lm_out$model, form.lm = lm_out, m = 5, printit = F) :

Diversity

## FULL MODEL

## Adjusted R2 is: -0.03

Fitting linear model: H_500 ~ om + gravel + sand + clay
	Estimate	Std. Error	t value	Pr(>\|t\|)
(Intercept)	0.05635	0.1667	0.3381	0.7376
om	0.4183	0.5073	0.8246	0.4159
gravel	0.2463	0.2483	0.9921	0.3288
sand	0.2698	0.507	0.5323	0.5983
clay	0.3124	0.2815	1.11	0.2756

## RMSE from cross-validation: 27.97158

Variance Inflation Factors
	om	gravel	sand	clay
VIF	2.3	1.55	2.93	1.76

## REDUCED MODEL

## Adjusted R2 is: 0

Fitting linear model: H_500 ~ 1
	Estimate	Std. Error	t value	Pr(>\|t\|)
(Intercept)	0.06334	0.1616	0.392	0.6975

## RMSE from cross-validation: 0.9736631

Quitting from lines 354-356 (C1_analyses_17B.Rmd) Error in Qr$qr[p1, p1, drop = FALSE] : indice hors limites De plus : Warning messages: 1: In CVlm(data = lm_out$model, form.lm = lm_out, m = 5, printit = F) :

2: In CVlm(data = lm_out$model, form.lm = lm_out, m = 5, printit = F) :

Evenness

## FULL MODEL

## Adjusted R2 is: 0.06

Fitting linear model: J_500 ~ om + gravel + sand + clay
	Estimate	Std. Error	t value	Pr(>\|t\|)
(Intercept)	0.006409	0.1518	0.04221	0.9666
om	0.9141	0.4621	1.978	0.05686
gravel	0.3201	0.2262	1.415	0.1669
sand	0.7476	0.4618	1.619	0.1156
clay	0.5227	0.2564	2.038	0.05012

## RMSE from cross-validation: 26.77056

Variance Inflation Factors
	om	gravel	sand	clay
VIF	2.3	1.55	2.93	1.76

## REDUCED MODEL

## Adjusted R2 is: 0.06

Fitting linear model: J_500 ~ om + gravel + sand + clay
	Estimate	Std. Error	t value	Pr(>\|t\|)
(Intercept)	0.006409	0.1518	0.04221	0.9666
om	0.9141	0.4621	1.978	0.05686
gravel	0.3201	0.2262	1.415	0.1669
sand	0.7476	0.4618	1.619	0.1156
clay	0.5227	0.2564	2.038	0.05012

## RMSE from cross-validation: 26.77056

Variance Inflation Factors
	om	gravel	sand	clay
VIF	2.3	1.55	2.93	1.76

Design 2

Richness

## FULL MODEL

## Adjusted R2 is: 0.21

Fitting linear model: S_500 ~ arsenic + cadmium + chromium + mercury + lead
	Estimate	Std. Error	t value	Pr(>\|t\|)
(Intercept)	-0.2519	0.2374	-1.061	0.3045
arsenic	-1.006	0.7414	-1.356	0.1938
cadmium	-0.1794	0.3118	-0.5752	0.5731
chromium	-0.6905	0.6333	-1.09	0.2917
mercury	-0.6837	0.489	-1.398	0.1812
lead	1.029	0.7637	1.347	0.1966

## RMSE from cross-validation: 1.145083

Variance Inflation Factors
	arsenic	cadmium	chromium	mercury	lead
VIF	2.11	1.6	3.14	1.22	3.69

## REDUCED MODEL

## Adjusted R2 is: 0.24

Fitting linear model: S_500 ~ arsenic + chromium + mercury + lead
	Estimate	Std. Error	t value	Pr(>\|t\|)
(Intercept)	-0.247	0.2326	-1.062	0.3031
arsenic	-1.014	0.7265	-1.396	0.1807
chromium	-0.8021	0.5908	-1.358	0.1923
mercury	-0.6267	0.4693	-1.335	0.1994
lead	0.985	0.7447	1.323	0.2035

## RMSE from cross-validation: 1.012635

Variance Inflation Factors
	arsenic	chromium	mercury	lead
VIF	2.11	2.99	1.2	3.67

Density

## FULL MODEL

## Adjusted R2 is: 0.18

Fitting linear model: N_500 ~ arsenic + cadmium + chromium + mercury + lead
	Estimate	Std. Error	t value	Pr(>\|t\|)
(Intercept)	-0.2115	0.2383	-0.8875	0.3879
arsenic	-0.6111	0.7441	-0.8212	0.4236
cadmium	0.4067	0.3129	1.3	0.2121
chromium	-0.07125	0.6356	-0.1121	0.9121
mercury	-0.7709	0.4908	-1.571	0.1358
lead	-0.1252	0.7665	-0.1633	0.8723

## RMSE from cross-validation: 1.056123

Variance Inflation Factors
	arsenic	cadmium	chromium	mercury	lead
VIF	2.11	1.6	3.14	1.22	3.69

## REDUCED MODEL

## Adjusted R2 is: 0.26

Fitting linear model: N_500 ~ arsenic + cadmium + mercury
	Estimate	Std. Error	t value	Pr(>\|t\|)
(Intercept)	-0.2439	0.2092	-1.166	0.2589
arsenic	-0.8016	0.4748	-1.688	0.1086
cadmium	0.3459	0.2472	1.399	0.1788
mercury	-0.8427	0.4205	-2.004	0.06036

## RMSE from cross-validation: 0.9536134

Variance Inflation Factors
	arsenic	cadmium	mercury
VIF	1.42	1.33	1.11

Diversity

## FULL MODEL

## Adjusted R2 is: 0.24

Fitting linear model: H_500 ~ arsenic + cadmium + chromium + mercury + lead
	Estimate	Std. Error	t value	Pr(>\|t\|)
(Intercept)	-0.2432	0.2299	-1.058	0.3059
arsenic	-1.098	0.7179	-1.529	0.1458
cadmium	-0.2655	0.3019	-0.8792	0.3923
chromium	-1.18	0.6132	-1.924	0.07233
mercury	-0.604	0.4735	-1.276	0.2203
lead	1.745	0.7395	2.359	0.03135	*

## RMSE from cross-validation: 1.218505

Variance Inflation Factors
	arsenic	cadmium	chromium	mercury	lead
VIF	2.11	1.6	3.14	1.22	3.69

## REDUCED MODEL

## Adjusted R2 is: 0.24

Fitting linear model: H_500 ~ arsenic + chromium + lead
	Estimate	Std. Error	t value	Pr(>\|t\|)
(Intercept)	-0.1355	0.2117	-0.6398	0.5304
arsenic	-1.021	0.7139	-1.43	0.1698
chromium	-1.287	0.5819	-2.212	0.04012	*
lead	1.434	0.7029	2.04	0.05632

## RMSE from cross-validation: 0.9705081

Variance Inflation Factors
	arsenic	chromium	lead
VIF	2.09	2.98	3.51

Evenness

## FULL MODEL

## Adjusted R2 is: -0.07

Fitting linear model: J_500 ~ arsenic + cadmium + chromium + mercury + lead
	Estimate	Std. Error	t value	Pr(>\|t\|)
(Intercept)	0.0006482	0.2717	0.002385	0.9981
arsenic	-0.2288	0.8484	-0.2697	0.7908
cadmium	-0.04213	0.3568	-0.1181	0.9075
chromium	-1.262	0.7247	-1.741	0.1008
mercury	0.04122	0.5595	0.07367	0.9422
lead	1.368	0.8739	1.565	0.1371

## RMSE from cross-validation: 1.475412

Variance Inflation Factors
	arsenic	cadmium	chromium	mercury	lead
VIF	2.11	1.6	3.14	1.22	3.69

## REDUCED MODEL

## Adjusted R2 is: 0.09

Fitting linear model: J_500 ~ chromium + lead
	Estimate	Std. Error	t value	Pr(>\|t\|)
(Intercept)	0.01992	0.2107	0.09453	0.9257
chromium	-1.294	0.6326	-2.045	0.055
lead	1.259	0.6494	1.938	0.06757

## RMSE from cross-validation: 1.348883

Variance Inflation Factors
	chromium	lead
VIF	2.98	2.98

3.3. Multivariate regressions

Independant variables are habitat parameters or heavy metal concentrations, dependant variables are species abundances. Variables have been standardized by mean and standard-deviation, and outliers and correlated variables have been excluded. Taxon densities were (log+1) transformed.

This analysis has been done on PRIMER, with a DistLM to identify the variables that explain the most the community variability and with a dbRDA to plot the results.

Design 1

Variables selected by the DistLM procedure have a $R^{2}$ of 0.23.

Design 2

Variables selected by the DistLM procedure have a $R^{2}$ of 0.13.

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